
# Author: Emilie Helen Wolf
# October 19, 2021


import numpy as np
np.random.seed(55)

import pandas as pd
pd.set_option('display.max_columns', None)
pd.set_option('display.max_rows', 200)

import matplotlib.pyplot as plt
import seaborn as sns
sns.set_style("darkgrid")
sns.set_context("talk")

from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split


# ignore warnings that might arise from plots
import warnings
warnings.filterwarnings("ignore")

# import the csv as a pandas DataFrame
df = pd.read_csv('used_phone_data.csv')
df.head()


df.info()

# Shape: 3571 x 15
# Nulls: 6 columns have missing values
# Types: float64(9), int64(2), object(4)

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 3571 entries, 0 to 3570
Data columns (total 15 columns):
 #   Column            Non-Null Count  Dtype  
---  ------            --------------  -----  
 0   brand_name        3571 non-null   object 
 1   os                3571 non-null   object 
 2   screen_size       3571 non-null   float64
 3   4g                3571 non-null   object 
 4   5g                3571 non-null   object 
 5   main_camera_mp    3391 non-null   float64
 6   selfie_camera_mp  3569 non-null   float64
 7   int_memory        3561 non-null   float64
 8   ram               3561 non-null   float64
 9   battery           3565 non-null   float64
 10  weight            3564 non-null   float64
 11  release_year      3571 non-null   int64  
 12  days_used         3571 non-null   int64  
 13  new_price         3571 non-null   float64
 14  used_price        3571 non-null   float64
dtypes: float64(9), int64(2), object(4)
memory usage: 418.6+ KB


# Count number of rows with at least one missing value
df.isnull().any(axis=1).sum()

# 203 rows with missing values

203


# Count how many values are missing in each column
df.isnull().sum()

# Look at the missingness
# 2 of the columns have the same number of missing values

brand_name            0
os                    0
screen_size           0
4g                    0
5g                    0
main_camera_mp      180
selfie_camera_mp      2
int_memory           10
ram                  10
battery               6
weight                7
release_year          0
days_used             0
new_price             0
used_price            0
dtype: int64


df[df['ram'].isnull()]

# These 10 Nokia phones from 2015 and 2016 are missing both ram and int_memory


# What are the int_memory and ram values for other Nokia phones in 2014 and 2017?

(df.loc[(df['brand_name']=='Nokia') & 
       ((df['release_year']==2014) | (df['release_year']==2017))]
     .groupby('release_year')['int_memory','ram'].describe())

# I think it's safe to replace all 10 with 32.0 and 4.0


# df[df['main_camera_mp'].isnull()].sample(n=10)

df[df['main_camera_mp'].isnull()].groupby(['release_year','brand_name'])['release_year'].count()

# Phones with missing main_camera_mp values are mostly newer models

release_year  brand_name
2017          OnePlus        2
2018          BlackBerry     4
              Coolpad        1
              OnePlus        3
              Panasonic      2
2019          Asus           4
              Coolpad        1
              Infinix        4
              Meizu         11
              OnePlus        8
              Realme        12
              Sony           5
2020          Coolpad        1
              Infinix        6
              Lava           2
              Meizu          4
              Motorola      18
              OnePlus        4
              Oppo          20
              Realme        24
              Sony           2
              Vivo          14
              Xiaomi        24
              ZTE            4
Name: release_year, dtype: int64


df[df['weight'].isnull()]

# These 7 XOLO phones from 2015 are missing weight


# What are the weights for other XOLO phones?

df.loc[(df['brand_name']=='XOLO')].groupby('release_year')['weight'].describe()

# Outside research says 2015 XOLO phones weight 125


df[df['battery'].isnull()]

# No pattern for battery nulls


# Let's look at a summary of all 62 Meizu phones

df.loc[(df['brand_name']=='Meizu')].groupby('release_year')['battery'].describe()

# The battery for the 3 Meizu are probably between 2400-3150mAh
# Outside research says: 3100 (147g), 3350(158g), 3140(145g)


df[df['selfie_camera_mp'].isnull()]

# Are these two Google phones missing a selfie camera????
# Outside research says the 2018 Google phone (Pixel 3) has a selfie camera with 8MP
# The other one matches the Pixel 3 XL, which has an 8MP selfie camera as well


# Look at all the objects and their unique values (discrete variables)

num_to_display = 35
for colname in df.dtypes[df.dtypes == 'object'].index:
    val_counts = df[colname].value_counts(dropna=False)
    print(val_counts[:num_to_display])
    if len(val_counts) > num_to_display:
        print(f'Only displaying first {num_to_display} of {len(val_counts)} values.')
    print('\n')

Others        509
Samsung       364
Huawei        264
LG            212
Lenovo        172
ZTE           141
Xiaomi        134
Oppo          129
Asus          126
Alcatel       125
Nokia         121
Micromax      120
Honor         118
Vivo          117
HTC           110
Motorola      110
Sony           88
Meizu          62
Apple          59
Gionee         56
Acer           51
XOLO           49
Panasonic      47
Realme         41
Celkon         37
Lava           36
Spice          30
Karbonn        30
OnePlus        22
BlackBerry     22
Coolpad        22
Microsoft      22
Google         15
Infinix        10
Name: brand_name, dtype: int64


Android    3246
Others      202
Windows      67
iOS          56
Name: os, dtype: int64


yes    2359
no     1212
Name: 4g, dtype: int64


no     3419
yes     152
Name: 5g, dtype: int64


df.describe().T

# Look at the statistical summaries of the continuous variables


for i in df.columns:
    sns.histplot(data=df, x=i)
    plt.show()
    
# Look at a histogram of each variable


df[df.duplicated()]

# Check for duplicates, none found


# Distribution of used prices

plt.figure(figsize=(8,5))

sns.violinplot(data=df, x='used_price');


# function to create labeled barplots


def labeled_barplot(data, feature, perc=True, n=None):
    """
    Barplot with percentage at the top

    data: dataframe
    feature: dataframe column
    perc: whether to display percentages instead of count (default is True)
    n: displays the top n category levels (default is None, i.e., display all levels)
    """

    total = len(data[feature])  # length of the column
    count = data[feature].nunique()
    if n is None:
        plt.figure(figsize=(count + 1, 5))
    else:
        plt.figure(figsize=(n + 1, 5))

    plt.xticks(rotation=90, fontsize=15)
    ax = sns.countplot(
        data=data,
        x=feature,
        palette="magma_r",
        order=data[feature].value_counts().index[:n].sort_values(),
    )

    for p in ax.patches:
        if perc == True:
            label = "{:.1f}%".format(
                100 * p.get_height() / total
            )  # percentage of each class of the category
        else:
            label = p.get_height()  # count of each level of the category

        x = p.get_x() + p.get_width() / 2  # width of the plot
        y = p.get_height()  # height of the plot

        ax.annotate(
            label,
            (x, y),
            ha="center",
            va="center",
            size=12,
            xytext=(0, 5),
            textcoords="offset points",
        )  # annotate the percentage

    plt.show()  # show the plot


df.columns

Index(['brand_name', 'os', 'screen_size', '4g', '5g', 'main_camera_mp',
       'selfie_camera_mp', 'int_memory', 'ram', 'battery', 'weight',
       'release_year', 'days_used', 'new_price', 'used_price'],
      dtype='object')


# What percentage of the used phone market is dominated by Android devices?



labeled_barplot(df, "os")

# 90.9%


labeled_barplot(df, "brand_name")


# Percent of each brand

df['brand_name'].value_counts(normalize=True)

Others        0.142537
Samsung       0.101932
Huawei        0.073929
LG            0.059367
Lenovo        0.048166
ZTE           0.039485
Xiaomi        0.037525
Oppo          0.036124
Asus          0.035284
Alcatel       0.035004
Nokia         0.033884
Micromax      0.033604
Honor         0.033044
Vivo          0.032764
HTC           0.030804
Motorola      0.030804
Sony          0.024643
Meizu         0.017362
Apple         0.016522
Gionee        0.015682
Acer          0.014282
XOLO          0.013722
Panasonic     0.013162
Realme        0.011481
Celkon        0.010361
Lava          0.010081
Spice         0.008401
Karbonn       0.008401
OnePlus       0.006161
BlackBerry    0.006161
Coolpad       0.006161
Microsoft     0.006161
Google        0.004201
Infinix       0.002800
Name: brand_name, dtype: float64


# What's the max ram available per release year?

plt.figure(figsize=(11,8))

sns.barplot(data=df, x='release_year', y='ram', estimator=np.max, ci=None, palette='turbo')
plt.title("Maximum Phone RAM Available by Release Year")
plt.xlabel("Release Year")
plt.ylabel("RAM in GB")
print(df.groupby('release_year')['ram'].max())

release_year
2013     4.0
2014     4.0
2015     4.0
2016     4.0
2017     4.0
2018     8.0
2019    16.0
2020    16.0
Name: ram, dtype: float64


# How many phones of each brand are available?

plt.figure(figsize=(25, 10))
sns.countplot(df['brand_name'], palette='magma_r', order = df['brand_name'].value_counts().index)
plt.title("Count of Used Phones by Brand");
plt.xticks(rotation=90);


# RAM by brand

plt.figure(figsize=(25, 10))
sns.barplot(data=df, 
            x='brand_name', 
            y='ram',
            palette='magma_r',
            order=df.groupby(['brand_name'])['ram'].mean().sort_values(ascending=False).index
           );
plt.xticks(rotation=90);
plt.title("Average RAM by brand");


# Comparison of Battery and Weight by Year

plt.figure(figsize=(15, 8))

sns.scatterplot(data=df, 
                x='weight', y='battery', hue='release_year', 
                palette='ch:start=.5,rot=-.75', 
                alpha=.5, legend='full'
             )
plt.title("Battery compared to Weight and Year");
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)

<matplotlib.legend.Legend at 0x1e78c40c610>


# Same scatterplot as above with screen_size added

plt.figure(figsize=(15, 10))

sns.scatterplot(data=df, 
                y='battery', 
                x='weight',
                #palette='ch:start=.5,rot=-.75',
                palette='coolwarm',
                alpha=.5, 
                legend='brief', 
                size='screen_size', 
                hue = 'release_year',
                sizes=(50,1000), 
               )
plt.title("Weight, Battery, Screen Size, and Release Year");
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.);


# What about new price compared to screen_size and main_camera_mp?

plt.figure(figsize=(15, 10))

sns.scatterplot(data=df, 
                y='new_price', 
                x='main_camera_mp',
                #palette='ch:start=.5,rot=-.75',
                palette='coolwarm',
                alpha=.5, 
                legend='brief', 
                size='screen_size', 
                hue = 'release_year',
                sizes=(50,1000), 
               )
plt.title("Title");
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.);


# Are there any light-weight phones with large batteries?

plt.figure(figsize=(13, 8))

sns.regplot(data=df[df['battery']>4500], y='weight', x='battery', marker='.')
plt.title("Weight of phones with batteries greater than 4500mAh");


# How many phones are available across different brands with a screen size larger than 6 inches?

# 6in = 15.24cm

plt.figure(figsize=(25, 10))
sns.countplot(data=df[df['screen_size']>15.24], x='brand_name', palette='magma_r',
             order = df[df['screen_size']>15.24].groupby(['brand_name'])['brand_name'].count().sort_values(ascending=False).index)
plt.title("Count of Used Phones by Brand that have screens larger than 6 inches");
plt.xticks(rotation=90);


# What is the distribution of budget phones offering greater than 8MP selfie cameras across brands?

plt.figure(figsize=(25, 10))
sns.countplot(data=df[df['selfie_camera_mp']>8], x='brand_name', palette='magma_r',
             order = df[df['selfie_camera_mp']>8].groupby(['brand_name'])['brand_name'].count().sort_values(ascending=False).index)
plt.title("Count of Used Phones by Brand that have greater than 8MP selfie cameras");
plt.xticks(rotation=90);

df[df['selfie_camera_mp']>8].groupby(['brand_name'])['brand_name'].count().sort_values(ascending=False)

brand_name
Huawei        91
Vivo          78
Oppo          75
Xiaomi        65
Samsung       60
Honor         43
Others        34
LG            32
Motorola      26
Meizu         24
ZTE           20
HTC           20
OnePlus       18
Realme        18
Sony          14
Lenovo        14
Nokia         10
Asus           6
Infinix        4
Gionee         4
Coolpad        3
Micromax       2
Panasonic      2
BlackBerry     2
Acer           1
Name: brand_name, dtype: int64


# Which attributes are highly correlated with the used phone price?

plt.figure(figsize = (25,12))
sns.heatmap(df.corr(), annot=True, vmin=-1, vmax=1, cmap='Spectral');

print(abs(df.corr())['used_price'].sort_values(ascending=False))

used_price          1.000000
new_price           0.926087
ram                 0.522659
selfie_camera_mp    0.497530
days_used           0.470760
release_year        0.456764
int_memory          0.404913
screen_size         0.385928
battery             0.363767
main_camera_mp      0.281065
weight              0.170654
Name: used_price, dtype: float64


# plt.figure(figsize = (25,15))
# sns.heatmap(abs(df.corr()), annot=True, vmin=0, vmax=1);


# How has the selfie camera resolution changed over the years?

plt.figure(figsize=(18, 7))

sns.pointplot(data=df,x='release_year',y='selfie_camera_mp', hue='os');


# What's the average used price of a phone for each release year?

plt.figure(figsize=(8,5))
sns.pointplot(data=df, x='release_year', y='used_price')

# The older the phone, the less it costs

<AxesSubplot:xlabel='release_year', ylabel='used_price'>


# Comparison of new vs used prices in relation to release_year

plt.figure(figsize=(15, 12))


sns.scatterplot(data=df, y='used_price', x='new_price', 
                palette='ch:start=.5,rot=-.75',
                hue='release_year', legend='full', alpha=.5);

plt.title("New vs Old Prices");
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.);


# What is the price difference between new and used?

df['percent_drop'] = 1 - df['used_price'] / df['new_price']

plt.figure(figsize=(8,5))
sns.pointplot(data=df, x='release_year', y='percent_drop')
plt.ylabel("Discount")

df.drop(['percent_drop'], axis=1, inplace=True)

# Phones before 2018 are discounted 60% or more on average!
# By comparison, phones from last year are only marked down an average of 30%


# Days used by OS

plt.figure(figsize=(25,10))
sns.boxplot(data=df, x='os', y='days_used', 
            #palette='magma_r',
            #order=df.groupby(['brand_name'])['days_used'].mean().sort_values(ascending=False).index
           );
plt.title("Days Used by Operating System");


# Days used by Year

plt.figure(figsize=(25,10))
sns.boxplot(data=df, x='release_year', y='days_used', 
           );
plt.title("Days Used by Release Year");


# How do the main and selfie cameras compare?

plt.figure(figsize=(13,8))
sns.scatterplot(data=df, x='main_camera_mp',y='selfie_camera_mp', hue='release_year', 
                palette='coolwarm', legend='full',)
plt.title("Main Camera vs Selfie Camera")
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.);


# For all phones with 5g, do they have 4g also?

print(df[df['5g']=='yes']['4g'].unique())

['yes']


# How many phones don't have 4g or 5g?

df[df['4g']=='no'].shape

(1212, 15)


sns.pairplot(data=df, hue='4g')

# all the orange dots represent "3G and Below"

<seaborn.axisgrid.PairGrid at 0x1e78ca9a040>


df.isnull().sum()

brand_name            0
os                    0
screen_size           0
4g                    0
5g                    0
main_camera_mp      180
selfie_camera_mp      2
int_memory           10
ram                  10
battery               6
weight                7
release_year          0
days_used             0
new_price             0
used_price            0
dtype: int64


# What are the int_memory and ram values for other Nokia phones in 2014 and 2017?

(df.loc[(df['brand_name']=='Nokia') & 
       ((df['release_year']==2014) | (df['release_year']==2017))]
     .groupby('release_year')['int_memory','ram'].describe())

# I think it's safe to replace all 10 with 32.0 and 4.0


# What are the weights for other XOLO phones?

df.loc[df['brand_name']=='XOLO'].groupby('release_year')['weight'].describe()

# Outside research says 2015 XOLO phones weigh 125


df[df['selfie_camera_mp'].isnull()]

# Are these two Google phones missing a selfie camera????
# Outside research says the 2018 Google phone (Pixel 3) has a selfie camera with 8MP
# The other one matches the Pixel 3 XL, which has an 8MP selfie camera as well


df[df['battery'].isnull()]

# The battery for the 3 Meizu are probably between 2400-3150mAh
# Outside research says: 3100 (147g), 3350(158g), 3140(145g)

# It looks like a Microsoft computer somehow got in the dataset...?


# How many smart phones weigh more than a pound? (454g)

df.loc[df['weight']>454].describe()

# 118 phones!!!


# Of those heavyweight phones, how many have missing values?

df.loc[df['weight']>454].isnull().any().sum()

1


# Which new cell phones costs more than $1800 / 1543€

df.loc[df['new_price']>1543]

# Some prices seem high, but they are reasonable enough considering the other specs


df[df['battery'].isnull()]

# These 3 are bizarre so they will be dropped


# Is there a pattern of missingness for the missing main_camera_mp values?

df[df['main_camera_mp'].isnull()].sort_values(by='new_price')

# We don't necesarrily want to drop these rows completely because most of them are newer models and 
# the dataset is predominately older data. Maybe we can just impute them.


df[df['main_camera_mp'].isnull()].groupby(['release_year','brand_name'])['release_year'].count()

# Phones with missing main_camera_mp values are mostly newer models

release_year  brand_name
2017          OnePlus        2
2018          BlackBerry     4
              Coolpad        1
              OnePlus        3
              Panasonic      2
2019          Asus           4
              Coolpad        1
              Infinix        4
              Meizu         11
              OnePlus        8
              Realme        12
              Sony           5
2020          Coolpad        1
              Infinix        6
              Lava           2
              Meizu          4
              Motorola      18
              OnePlus        4
              Oppo          20
              Realme        24
              Sony           2
              Vivo          14
              Xiaomi        24
              ZTE            4
Name: release_year, dtype: int64


# What's the average main_camera_mp per brand in 2020?

print(df.groupby(['release_year'])['main_camera_mp','selfie_camera_mp','new_price'].median())

df[df['release_year']>2017].groupby(['release_year','brand_name'])['main_camera_mp','selfie_camera_mp','new_price'].max()

# 2020 Oppo main cameras, upon research: 12MP, 48MP, 13MP, 48MP, 48MP

# If it's from 2020 and the new price > 500, then main_mp = 48mp
# If it's from 2019 and the new price > 900, then main_mp = 48mp
# If new price < 100, then main_mp = 1
# If new price < 200, then main_mp = 8
# ELSE main_mp = 12

              main_camera_mp  selfie_camera_mp  new_price
release_year                                             
2013                     5.0               1.0  141.12000
2014                     8.0               2.0  169.94500
2015                     8.0               5.0  171.31000
2016                    13.0               5.0  198.19000
2017                    13.0               8.0  200.97000
2018                    13.0               8.0  250.05000
2019                    12.0              16.0  237.99150
2020                     8.0              13.0  237.14675


# Which phones have cameras above 30MP?

df.loc[(df['main_camera_mp']>40) | (df['selfie_camera_mp']>40)].sort_values(by='release_year')

# We can believe that newer phones might have smaller cameras, but it's
# hard to believe that older phones have larger cameras.

# The top one from 2013 looks suspicious, but I looked it up and it's factual https://en.wikipedia.org/wiki/Nokia_Lumia_1020


df['int_memory'].fillna(32.0, inplace=True)
df['ram'].fillna(4.0, inplace=True)

df.iloc[3113:3120,10].fillna(125.0, inplace=True) # all weights for Nokia
df.iloc[1131:1133,6].fillna(8.0, inplace=True) # selfie_camera_mp for Google phones
df.iloc[1901,9]=3140 # Meizu battery
df.iloc[1903,9]=3350 # Meizu battery
df.iloc[1904,9]=3100 # Meizu battery


# If it's from 2020 and the new price > 500, then main_mp = 48mp
# If it's from 2019 and the new price > 900, then main_mp = 20mp
# If new price < 100, then main_mp = 1
# If new price < 200, then main_mp = 6
# ELSE main_mp = 12

df.loc[(df['release_year']==2020) & (df['new_price']>500),'main_camera_mp'].fillna(48, inplace=True)
df.loc[(df['release_year']==2019) & (df['new_price']>900), 'main_camera_mp'].fillna(20, inplace=True)
df.loc[df['new_price']<100,'main_camera_mp'].fillna(1, inplace=True)
df.loc[df['new_price']<200,'main_camera_mp'].fillna(6, inplace=True)
df['main_camera_mp'].fillna(12, inplace=True)


# drop the remaining 3 rows with missing values
df = df.dropna()


# Battery Outlier? Drop it

print(df[df['battery']>10000])

df.drop(387,inplace=True)

print(df.isnull().sum())
print(df.shape)
print(df.info())

    brand_name       os  screen_size   4g  5g  main_camera_mp  \
387    Samsung  Android        43.66  yes  no            12.0   

     selfie_camera_mp  int_memory  ram  battery  weight  release_year  \
387               5.0        64.0  3.0  12000.0    23.0          2019   

     days_used  new_price  used_price  
387        266     659.47      460.58  
brand_name          0
os                  0
screen_size         0
4g                  0
5g                  0
main_camera_mp      0
selfie_camera_mp    0
int_memory          0
ram                 0
battery             0
weight              0
release_year        0
days_used           0
new_price           0
used_price          0
dtype: int64
(3567, 15)
<class 'pandas.core.frame.DataFrame'>
Int64Index: 3567 entries, 0 to 3570
Data columns (total 15 columns):
 #   Column            Non-Null Count  Dtype  
---  ------            --------------  -----  
 0   brand_name        3567 non-null   object 
 1   os                3567 non-null   object 
 2   screen_size       3567 non-null   float64
 3   4g                3567 non-null   object 
 4   5g                3567 non-null   object 
 5   main_camera_mp    3567 non-null   float64
 6   selfie_camera_mp  3567 non-null   float64
 7   int_memory        3567 non-null   float64
 8   ram               3567 non-null   float64
 9   battery           3567 non-null   float64
 10  weight            3567 non-null   float64
 11  release_year      3567 non-null   int64  
 12  days_used         3567 non-null   int64  
 13  new_price         3567 non-null   float64
 14  used_price        3567 non-null   float64
dtypes: float64(9), int64(2), object(4)
memory usage: 445.9+ KB
None


# We already dropped the most extreme outlier.
# Now let's try dropping other outliers

# We don't want ram to be affected, so we'll change it to a category and then back to float
df['ram'] = df['ram'].astype('category')


def treat_outliers(df, col):
    """
    treats outliers in a variable
    col: str, name of the numerical variable
    df: dataframe
    col: name of the column
    """
    Q1 = df[col].quantile(0.25)  # 25th quantile
    Q3 = df[col].quantile(0.75)  # 75th quantile
    IQR = Q3 - Q1
    Lower_Whisker = Q1 - 2 * IQR
    Upper_Whisker = Q3 + 2 * IQR

    # all the values smaller than Lower_Whisker will be assigned the value of Lower_Whisker
    # all the values greater than Upper_Whisker will be assigned the value of Upper_Whisker
    df[col] = np.clip(df[col], Lower_Whisker, Upper_Whisker)

    return df


def treat_outliers_all(df, col_list):
    """
    treat outlier in all numerical variables
    col_list: list of numerical variables
    df: data frame
    """
    for c in col_list:
        df = treat_outliers(df, c)

    return df

# treating the outliers
numerical_col = df.select_dtypes(include=np.number).columns.tolist()
df = treat_outliers_all(df, numerical_col)
df.shape

df['ram'] = df['ram'].astype('float64')


# Now to change 4g and 5g to 1s and 0s............

df['4g'] = df['4g'].map(dict(yes=1, no=0))
df['5g'] = df['5g'].map(dict(yes=1, no=0))

df["4g"] = df["4g"].astype('int64')
df["5g"] = df["5g"].astype('int64')


df[['4g','5g']].info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 3567 entries, 0 to 3570
Data columns (total 2 columns):
 #   Column  Non-Null Count  Dtype
---  ------  --------------  -----
 0   4g      3567 non-null   int64
 1   5g      3567 non-null   int64
dtypes: int64(2)
memory usage: 83.6 KB


plt.figure(figsize = (25,12))
sns.heatmap(df.corr(), annot=True, vmin=-1, vmax=1, cmap='Spectral');

print(abs(df.corr())['used_price'].sort_values(ascending=False))

used_price          1.000000
new_price           0.910208
selfie_camera_mp    0.633421
int_memory          0.583849
days_used           0.551348
release_year        0.537556
ram                 0.505263
screen_size         0.490430
5g                  0.473231
battery             0.465321
4g                  0.453054
main_camera_mp      0.422298
weight              0.311568
Name: used_price, dtype: float64


for i in df.columns:
    sns.histplot(data=df, x=i, kde=True)
    plt.show()
    

# plt.figure(figsize=(25,12))
# sns.pairplot(data=df)


# We will remove brand_name and OS

df.drop(['brand_name'], axis=1, inplace=True)
df.drop(['os'], axis=1, inplace=True)

df.head()


# Then we split the data, build the model, and test it

X = df.drop(['used_price'], axis=1)
y = df['used_price'].copy()

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.30, random_state=55)

regression_model = LinearRegression()
regression_model.fit(X_train, y_train)

print(regression_model.score(X_train, y_train))
print(regression_model.score(X_test, y_test))

0.953073372668335
0.9578846114455567


# This model captures 95% of the test data!!!

# NOTE: We tested this model without the IQR Outlier treatment as well, and the model was still 95%,
# so we are keeping the outlier treatment

# Let's check the Adjusted R Squared and more

from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score


# function to compute adjusted R-squared
def adj_r2_score(predictors, targets, predictions):
    r2 = r2_score(targets, predictions)
    n = predictors.shape[0]
    k = predictors.shape[1]
    return 1 - ((1 - r2) * (n - 1) / (n - k - 1))


# function to compute MAPE
def mape_score(targets, predictions):
    return np.mean(np.abs(targets - predictions) / targets) * 100


# function to compute different metrics to check performance of a regression model
def model_performance_regression(model, predictors, target):
    """
    Function to compute different metrics to check regression model performance

    model: regressor
    predictors: independent variables
    target: dependent variable
    """

    # predicting using the independent variables
    pred = model.predict(predictors)

    r2 = r2_score(target, pred)  # to compute R-squared
    adjr2 = adj_r2_score(predictors, target, pred)  # to compute adjusted R-squared
    rmse = np.sqrt(mean_squared_error(target, pred))  # to compute RMSE
    mae = mean_absolute_error(target, pred)  # to compute MAE
    mape = mape_score(target, pred)  # to compute MAPE

    # creating a dataframe of metrics
    df_perf = pd.DataFrame(
        {
            "RMSE": rmse,
            "MAE": mae,
            "R-squared": r2,
            "Adj. R-squared": adjr2,
            "MAPE": mape,
        },
        index=[0],
    )

    return df_perf


# checking model performance on train set (seen 70% data)
print("Training Performance\n")
linearregression_train_perf = model_performance_regression(
    regression_model, X_train, y_train
)
print(linearregression_train_perf)

print()

# checking model performance on test set (seen 30% data)
print("Test Performance\n")
linearregression_test_perf = model_performance_regression(
    regression_model, X_test, y_test
)
print(linearregression_test_perf)

Training Performance

        RMSE       MAE  R-squared  Adj. R-squared      MAPE
0  15.662613  11.18816   0.953073        0.952847  19.54726

Test Performance

        RMSE        MAE  R-squared  Adj. R-squared       MAPE
0  15.300164  10.861353   0.957885        0.957407  17.898905


from statsmodels.stats.outliers_influence import variance_inflation_factor

# we will define a function to check VIF
def checking_vif(predictors):
    vif = pd.DataFrame()
    vif["feature"] = predictors.columns

    # calculating VIF for each feature
    vif["VIF"] = [
        variance_inflation_factor(predictors.values, i)
        for i in range(len(predictors.columns))
    ]
    return vif

checking_vif(X_train)


y_train.head()

1472     68.37
127     260.19
907      44.88
2200     92.35
1216     74.99
Name: used_price, dtype: float64


def dropRetest(cols):

    for i in cols:
        X_train_1 = X_train.drop([i], axis=1)

        regression_model_1 = LinearRegression()
        regression_model_1.fit(X_train_1, y_train)

        linearregression_train_perf_1 = model_performance_regression(regression_model_1, X_train_1, y_train)
        print('Removing '+i)
        print(linearregression_train_perf_1)
        print()
    
    
cols=['release_year','battery','screen_size','ram','weight','days_used','main_camera_mp']

dropRetest(cols)

Removing release_year
        RMSE        MAE  R-squared  Adj. R-squared       MAPE
0  15.666531  11.185398    0.95305        0.952842  19.513303

Removing battery
        RMSE        MAE  R-squared  Adj. R-squared       MAPE
0  15.662936  11.189263   0.953071        0.952864  19.548804

Removing screen_size
        RMSE       MAE  R-squared  Adj. R-squared       MAPE
0  15.663547  11.18734   0.953068         0.95286  19.548575

Removing ram
        RMSE        MAE  R-squared  Adj. R-squared       MAPE
0  15.724886  11.246621   0.952699         0.95249  19.715815

Removing weight
        RMSE        MAE  R-squared  Adj. R-squared       MAPE
0  15.664573  11.188646   0.953062        0.952854  19.550897

Removing days_used
        RMSE        MAE  R-squared  Adj. R-squared       MAPE
0  21.279293  15.961124   0.913383        0.912999  21.861876

Removing main_camera_mp
        RMSE        MAE  R-squared  Adj. R-squared       MAPE
0  15.687998  11.216255   0.952921        0.952713  19.649139


X_train_2 = X_train.drop(['battery'], axis=1)

checking_vif(X_train_2)


X_train_2 = X_train.drop(['weight'], axis=1)

checking_vif(X_train_2)


        X_train_2 = X_train.drop(['battery','weight'], axis=1)

        regression_model_2 = LinearRegression()
        regression_model_2.fit(X_train_2, y_train)

        linearregression_train_perf_2 = model_performance_regression(regression_model_2, X_train_2, y_train)
        print('Removing both battery and weight')
        print(linearregression_train_perf_2)
        print()

Removing both battery and weight
        RMSE        MAE  R-squared  Adj. R-squared       MAPE
0  15.664621  11.188262   0.953061        0.952872  19.550816


# Let's check the TEST set by removing weight and battery too

X_test_2 = X_test.drop(['battery','weight'], axis=1)

linearregression_test_perf_2 = model_performance_regression(regression_model_2, X_test_2, y_test)
print('Removing both battery and weight')
print(linearregression_test_perf_2)
print()

Removing both battery and weight
        RMSE       MAE  R-squared  Adj. R-squared       MAPE
0  15.292189  10.85801   0.957929        0.957532  17.882971


import statsmodels.api as sm

# unlike sklearn, statsmodels does not add a constant to the data on its own
# we have to add the constant manually
x_train1 = sm.add_constant(X_train_2)
# adding constant to the test data
x_test1 = sm.add_constant(X_test_2)

olsmod2 = sm.OLS(y_train, x_train1).fit()


# let us create a dataframe with actual, fitted and residual values
df_pred = pd.DataFrame()

df_pred["Actual Values"] = y_train  # actual values
df_pred["Fitted Values"] = olsmod2.fittedvalues  # predicted values
df_pred["Residuals"] = olsmod2.resid  # residuals

df_pred.head()


# let's plot the fitted values vs residuals

sns.residplot(
    data=df_pred, x="Fitted Values", y="Residuals", color="purple", lowess=True
)
plt.xlabel("Fitted Values")
plt.ylabel("Residuals")
plt.title("Fitted vs Residual plot")
plt.show()


sns.histplot(data=df_pred, x="Residuals", kde=True)
plt.title("Normality of residuals")
plt.show()

# There is a bell curve


import pylab
import scipy.stats as stats

stats.probplot(df_pred["Residuals"], dist="norm", plot=pylab)
plt.show()


stats.shapiro(df_pred["Residuals"])

ShapiroResult(statistic=0.9476568102836609, pvalue=6.163355591350064e-29)


import statsmodels.stats.api as sms
from statsmodels.compat import lzip

name = ["F statistic", "p-value"]
test = sms.het_goldfeldquandt(df_pred["Residuals"], X_train_2)
lzip(name, test)

[('F statistic', 1.0199143827807882), ('p-value', 0.364359396111027)]


olsmodel_final = sm.OLS(y_test, x_test1).fit()
print(olsmodel_final.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:             used_price   R-squared:                       0.959
Model:                            OLS   Adj. R-squared:                  0.958
Method:                 Least Squares   F-statistic:                     2464.
Date:                Fri, 22 Oct 2021   Prob (F-statistic):               0.00
Time:                        23:07:34   Log-Likelihood:                -4430.0
No. Observations:                1071   AIC:                             8882.
Df Residuals:                    1060   BIC:                             8937.
Df Model:                          10                                         
Covariance Type:            nonrobust                                         
====================================================================================
                       coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------
const            -1574.0019    885.697     -1.777      0.076   -3311.921     163.917
screen_size          0.4316      0.126      3.415      0.001       0.184       0.680
4g                  -3.3511      1.482     -2.261      0.024      -6.260      -0.443
5g                   5.3879      3.022      1.783      0.075      -0.542      11.317
main_camera_mp      -0.4349      0.141     -3.095      0.002      -0.711      -0.159
selfie_camera_mp     0.5590      0.147      3.794      0.000       0.270       0.848
int_memory           0.0821      0.016      5.175      0.000       0.051       0.113
ram                  1.2128      0.469      2.584      0.010       0.292       2.134
release_year         0.8083      0.439      1.840      0.066      -0.054       1.670
days_used           -0.0854      0.003    -28.509      0.000      -0.091      -0.080
new_price            0.3901      0.004     87.414      0.000       0.381       0.399
==============================================================================
Omnibus:                      148.058   Durbin-Watson:                   1.881
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              474.956
Skew:                           0.672   Prob(JB):                    7.32e-104
Kurtosis:                       5.973   Cond. No.                     4.07e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 4.07e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

	count	mean	std	min	25%	50%	75%	max
release_year
2013	24.0	175.116667	84.293572	116.0	140.0	148.85	160.25	480.0
2014	18.0	118.888889	4.714045	100.0	120.0	120.00	120.00	120.0
2015	0.0	NaN	NaN	NaN	NaN	NaN	NaN	NaN

	count	mean	std	min	25%	50%	75%	max
release_year
2013	1.0	2400.000000	NaN	2400.0	2400.00	2400.0	2400.00	2400.0
2014	0.0	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2015	6.0	3005.000000	250.000000	2500.0	3061.25	3095.0	3128.75	3150.0
2016	14.0	3047.857143	196.436663	2560.0	3060.00	3060.0	3060.00	3400.0
2017	7.0	3315.000000	359.525150	3000.0	3035.00	3235.0	3450.00	4000.0
2018	16.0	3188.750000	215.031006	3000.0	3000.00	3100.0	3315.00	3600.0
2019	11.0	3945.454545	332.757078	3600.0	3600.00	4000.0	4000.00	4500.0
2020	4.0	4500.000000	0.000000	4500.0	4500.00	4500.0	4500.00	4500.0

	count	mean	std	min	25%	50%	75%	max
screen_size	3571.0	14.803892	5.153092	2.700	12.700	13.49	16.510	46.36
main_camera_mp	3391.0	9.400454	4.818396	0.080	5.000	8.00	13.000	48.00
selfie_camera_mp	3569.0	6.547352	6.879359	0.300	2.000	5.00	8.000	32.00
int_memory	3561.0	54.532607	84.696246	0.005	16.000	32.00	64.000	1024.00
ram	3561.0	4.056962	1.391844	0.030	4.000	4.00	4.000	16.00
battery	3565.0	3067.225666	1364.206665	80.000	2100.000	3000.00	4000.000	12000.00
weight	3564.0	179.424285	90.280856	23.000	140.000	159.00	184.000	950.00
release_year	3571.0	2015.964996	2.291784	2013.000	2014.000	2016.00	2018.000	2020.00
days_used	3571.0	675.391487	248.640972	91.000	536.000	690.00	872.000	1094.00
new_price	3571.0	237.389037	197.545581	9.130	120.130	189.80	291.935	2560.20
used_price	3571.0	109.880277	121.501226	2.510	45.205	75.53	126.000	1916.54

	count	mean	std	min	25%	50%	75%	max
release_year
2013	24.0	175.116667	84.293572	116.0	140.0	148.85	160.25	480.0
2014	18.0	118.888889	4.714045	100.0	120.0	120.00	120.00	120.0
2015	0.0	NaN	NaN	NaN	NaN	NaN	NaN	NaN

	screen_size	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
count	118.000000	118.000000	118.000000	118.000000	118.000000	117.000000	118.000000	118.000000	118.000000	118.000000	118.000000
mean	25.905254	7.261864	3.319492	53.559322	4.008475	6658.952991	551.768644	2015.720339	698.500000	342.040424	152.202881
std	2.478659	3.543887	2.554007	130.980297	0.745307	2027.739652	97.326595	2.371071	246.042097	188.021090	117.907108
min	13.490000	0.300000	0.300000	16.000000	1.000000	1200.000000	456.000000	2013.000000	139.000000	99.960000	35.980000
25%	25.560000	5.000000	1.300000	16.000000	4.000000	5770.500000	480.750000	2014.000000	549.000000	220.415000	78.005000
50%	25.560000	8.000000	2.000000	32.000000	4.000000	7000.000000	510.000000	2015.000000	697.500000	298.550000	112.485000
75%	26.040000	8.000000	5.000000	32.000000	4.000000	8000.000000	615.000000	2018.000000	901.250000	390.612500	186.972500
max	33.500000	16.000000	8.000000	1024.000000	6.000000	9720.000000	950.000000	2020.000000	1089.000000	1100.860000	749.840000

Importing necessary libraries and data¶

Data Overview¶

Questions¶

FIRST LOOK¶

Initial Observations¶

Exploratory Data Analysis (EDA)¶

Observation: Most used phones are under 500 Euros and there appears to be some cosing 2000¶

The top available brands are Samsung, Huawei, LG, and Lenovo¶

Observation: It looks like 4GB RAM phones from older years are still available, which could useful for customers on a budget¶

Observation: There appears to be an outlier in the top left. How can a phone with an enormous battery and screen size weigh so little?¶

Observation: There is a positive relationship, but it's not as obvious because most of the main cameras that have 10-12GB have a very wide spread in new price. It also seems like most of the newer models in the dataset stay in the 8-12GB range¶

There are some lightweight phones available with large batteries, but mostly as the battery increases, so does the weight¶

Observation: There is a good amount of availability of phones from many different brands that have screen sizes greater than 6 inches¶

Observations¶

The Selfie Cameras get better year after year, for all operating systems¶

Observation: A lot of the newer models have been used less so they might be in better condition¶

Observation: The Selfie camera has gotten way better in recent years while the main camera has not¶

Questions¶

Data Preprocessing¶

We already checked for duplicates and there are none. Moving on to check for missing values.¶

Replacing/Dropping missing values and outliers¶

EDA¶

Observation: The correlation values changed but the positive/negative signs did not¶

Observation: Everything looks good and we can tell that outliers were capped. We will build and test the model with and without outlier treatment in the next step¶

Building a Linear Regression model¶

Model performance evaluation¶

Observation: The first model does really well with the testing set at .957¶

Checking Linear Regression Assumptions¶

TEST FOR MULTICOLLINEARITY¶

TEST FOR LINEARITY AND INDEPENDENCE¶

We see no pattern in the plot above. Hence, the assumptions of linearity and independence are satisfied.¶

TEST FOR NORMALITY¶

TEST FOR HOMOSCEDASTICITY¶

Final Model Summary¶

Including all the Coefficients¶

The final linear model captures up to 96% of the test data¶

Here's what we did:¶

Observations¶

Actionable Insights and Recommendations¶

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
0	Honor	Android	23.97	yes	no	13.0	5.0	64.0	3.0	3020.0	146.0	2020	127	111.62	86.96
1	Honor	Android	28.10	yes	yes	13.0	16.0	128.0	8.0	4300.0	213.0	2020	325	249.39	161.49
2	Honor	Android	24.29	yes	yes	13.0	8.0	128.0	8.0	4200.0	213.0	2020	162	359.47	268.55
3	Honor	Android	26.04	yes	yes	13.0	8.0	64.0	6.0	7250.0	480.0	2020	345	278.93	180.23
4	Honor	Android	15.72	yes	no	13.0	8.0	64.0	3.0	5000.0	185.0	2020	293	140.87	103.80

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
2140	Nokia	Others	5.72	no	no	0.3	0.3	NaN	NaN	NaN	81.0	2016	815	29.21	8.65
2141	Nokia	Others	5.72	no	no	0.3	0.3	NaN	NaN	NaN	82.6	2016	1023	38.78	11.42
2142	Nokia	Others	6.35	no	no	2.0	2.0	NaN	NaN	1200.0	91.8	2015	867	68.01	20.46
2143	Nokia	Others	6.35	no	no	2.0	2.0	NaN	NaN	1200.0	91.8	2015	772	69.94	28.06
2144	Nokia	Others	5.72	no	no	2.0	2.0	NaN	NaN	1100.0	79.0	2015	1012	41.92	12.52
2145	Nokia	Others	5.72	no	no	2.0	2.0	NaN	NaN	1100.0	79.0	2015	798	40.48	16.13
2146	Nokia	Others	3.18	no	no	2.0	2.0	NaN	NaN	800.0	69.6	2015	1009	19.92	6.07
2147	Nokia	Others	3.18	no	no	2.0	2.0	NaN	NaN	800.0	69.8	2015	665	18.48	7.48
2148	Nokia	Others	5.72	no	no	0.3	2.0	NaN	NaN	1100.0	78.4	2015	559	29.33	14.76
2149	Nokia	Others	5.72	no	no	0.3	2.0	NaN	NaN	1100.0	78.6	2015	682	30.00	12.03

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
3113	XOLO	Android	12.70	yes	no	13.0	5.0	32.0	4.0	2400.0	NaN	2015	576	138.44	69.38
3114	XOLO	Android	13.49	yes	no	8.0	5.0	16.0	4.0	3200.0	NaN	2015	800	179.33	53.81
3115	XOLO	Android	12.70	no	no	8.0	2.0	32.0	4.0	2100.0	NaN	2015	878	59.21	17.77
3116	XOLO	Android	10.95	no	no	5.0	0.3	32.0	4.0	1800.0	NaN	2015	1036	81.13	24.32
3117	XOLO	Android	12.70	no	no	5.0	0.3	16.0	4.0	2500.0	NaN	2015	679	77.26	30.85
3118	XOLO	Windows	12.70	no	no	8.0	2.0	32.0	4.0	2200.0	NaN	2015	838	120.51	36.14
3119	XOLO	Android	12.70	no	no	8.0	5.0	32.0	4.0	2500.0	NaN	2015	1045	119.75	35.78

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
1901	Meizu	Android	13.49	yes	no	13.0	5.0	16.0	4.0	NaN	145.0	2014	986	129.49	38.67
1903	Meizu	Android	13.49	yes	no	20.7	5.0	16.0	4.0	NaN	158.0	2014	1043	399.67	119.86
1904	Meizu	Android	18.42	yes	no	20.7	2.0	16.0	4.0	NaN	147.0	2014	1007	339.04	101.65
2037	Microsoft	Windows	26.35	no	no	5.0	3.5	32.0	4.0	NaN	675.9	2013	931	331.21	99.49
2140	Nokia	Others	5.72	no	no	0.3	0.3	NaN	NaN	NaN	81.0	2016	815	29.21	8.65
2141	Nokia	Others	5.72	no	no	0.3	0.3	NaN	NaN	NaN	82.6	2016	1023	38.78	11.42

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
1131	Google	Android	15.72	yes	no	12.2	NaN	64.0	4.0	3430.0	184.0	2018	475	959.08	479.52
1132	Google	Android	13.49	yes	no	12.2	NaN	64.0	4.0	2915.0	148.0	2018	424	849.87	425.16

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
45	Huawei	Android	23.65	yes	yes	13.0	16.0	512.0	12.0	4500.0	198.0	2019	289	1699.36	1185.73
204	Xiaomi	Android	32.39	yes	yes	12.0	20.0	512.0	12.0	4050.0	241.0	2019	478	2498.24	1248.99
270	Huawei	Android	23.65	yes	yes	13.0	16.0	512.0	12.0	4500.0	198.0	2019	488	1701.54	850.85
1313	Huawei	Android	20.32	yes	no	13.0	16.0	512.0	4.0	4500.0	295.0	2019	434	2300.87	1150.41
1325	Huawei	Android	21.43	yes	no	13.0	24.0	256.0	4.0	4200.0	187.0	2018	365	1600.29	1039.60
2448	Samsung	Android	18.26	yes	no	12.0	9.0	512.0	4.0	4380.0	263.0	2019	428	1751.18	875.62
3320	Huawei	Android	20.32	yes	yes	10.5	16.0	512.0	8.0	4500.0	300.0	2020	248	2560.20	1916.54
3463	Huawei	Android	20.32	yes	yes	10.5	16.0	512.0	8.0	4500.0	300.0	2020	129	2560.20	1916.34

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
145	Realme	Android	15.40	yes	no	NaN	5.0	32.0	3.0	4000.0	166.0	2020	167	40.0800	30.34
370	Realme	Android	15.40	yes	no	NaN	5.0	32.0	3.0	4000.0	166.0	2020	247	40.8500	30.68
65	Lava	Android	23.97	yes	no	NaN	5.0	32.0	2.0	3200.0	150.0	2020	356	79.9200	51.87
290	Lava	Android	23.97	yes	no	NaN	5.0	32.0	2.0	3200.0	150.0	2020	359	79.9400	51.77
200	Xiaomi	Android	18.73	yes	no	NaN	8.0	32.0	2.0	5000.0	188.0	2020	321	80.8200	52.13
3341	Motorola	Android	15.40	yes	no	NaN	5.0	32.0	2.0	3000.0	160.0	2020	208	82.3225	60.90
3484	Motorola	Android	15.40	yes	no	NaN	5.0	32.0	2.0	3000.0	160.0	2020	249	82.3225	60.74
287	Infinix	Android	16.19	yes	no	NaN	8.0	32.0	2.0	5000.0	185.0	2020	329	88.8800	57.95
199	Xiaomi	Android	18.73	yes	no	NaN	8.0	32.0	2.0	5000.0	188.0	2020	265	89.6000	68.99
62	Infinix	Android	16.19	yes	no	NaN	8.0	32.0	2.0	5000.0	185.0	2020	256	90.5100	66.43
60	Infinix	Android	28.26	yes	no	NaN	8.0	32.0	2.0	6000.0	209.0	2020	245	99.2500	72.93
369	Realme	Android	16.03	yes	no	NaN	5.0	32.0	3.0	5000.0	195.0	2020	321	99.5300	65.02
371	Realme	Android	15.40	yes	no	NaN	5.0	32.0	2.0	4000.0	166.0	2019	450	99.5900	49.75
63	Infinix	Android	16.19	yes	no	NaN	16.0	32.0	3.0	4000.0	178.0	2019	316	99.7000	64.51
285	Infinix	Android	28.26	yes	no	NaN	8.0	32.0	2.0	6000.0	209.0	2020	320	100.0200	65.22
288	Infinix	Android	16.19	yes	no	NaN	16.0	32.0	3.0	4000.0	178.0	2019	356	100.0800	63.94
144	Realme	Android	16.03	yes	no	NaN	5.0	32.0	3.0	5000.0	195.0	2020	111	100.1400	76.16
146	Realme	Android	15.40	yes	no	NaN	5.0	32.0	2.0	4000.0	166.0	2019	399	100.6200	65.48
202	Xiaomi	Others	8.73	no	no	NaN	16.0	64.0	6.0	420.0	208.0	2020	153	101.9500	75.34
3522	Realme	Android	16.03	yes	no	NaN	5.0	32.0	2.0	5000.0	195.0	2020	279	106.1990	66.83
3379	Realme	Android	16.03	yes	no	NaN	5.0	32.0	2.0	5000.0	195.0	2020	357	106.1990	67.78
286	Infinix	Android	16.19	yes	no	NaN	8.0	64.0	4.0	5000.0	185.0	2020	173	110.1800	82.67
3407	Xiaomi	Android	23.65	yes	no	NaN	8.0	32.0	3.0	5020.0	198.0	2020	340	110.5000	72.53
61	Infinix	Android	16.19	yes	no	NaN	8.0	64.0	4.0	5000.0	185.0	2020	173	111.2500	85.94
3524	Realme	Android	23.50	yes	no	NaN	8.0	32.0	3.0	5000.0	195.0	2020	113	118.9915	91.43
3381	Realme	Android	23.50	yes	no	NaN	8.0	32.0	3.0	5000.0	195.0	2020	278	118.9915	72.50
130	Oppo	Android	15.56	yes	no	NaN	8.0	64.0	3.0	4230.0	168.0	2020	273	119.4000	82.49
355	Oppo	Android	15.56	yes	no	NaN	8.0	64.0	3.0	4230.0	168.0	2020	267	119.8100	80.64
3483	Motorola	Android	16.03	yes	no	NaN	8.0	64.0	4.0	5000.0	200.0	2020	277	122.4000	84.73
3340	Motorola	Android	16.03	yes	no	NaN	8.0	64.0	4.0	5000.0	200.0	2020	352	122.4000	80.04
3339	Motorola	Android	15.56	yes	no	NaN	5.0	32.0	2.0	3550.0	185.0	2020	174	127.4915	95.61
3482	Motorola	Android	15.56	yes	no	NaN	5.0	32.0	2.0	3550.0	185.0	2020	230	127.4915	93.86
289	Infinix	Android	15.56	yes	no	NaN	16.0	32.0	2.0	4000.0	165.0	2019	497	129.8100	64.91
64	Infinix	Android	15.56	yes	no	NaN	16.0	32.0	2.0	4000.0	165.0	2019	468	130.4900	65.29
3411	Xiaomi	Android	23.65	yes	no	NaN	13.0	64.0	3.0	5020.0	199.0	2020	208	136.0000	104.57
3376	Realme	Android	16.03	yes	no	NaN	16.0	64.0	3.0	5000.0	199.0	2020	320	139.5190	90.68
3519	Realme	Android	16.03	yes	no	NaN	16.0	64.0	3.0	5000.0	199.0	2020	206	139.5190	101.97
3529	Realme	Android	15.72	yes	no	NaN	25.0	64.0	4.0	4045.0	172.0	2019	288	143.5650	107.38
3386	Realme	Android	15.72	yes	no	NaN	25.0	64.0	4.0	4045.0	172.0	2019	277	143.5650	98.09
3525	Realme	Android	16.03	yes	no	NaN	13.0	64.0	4.0	5000.0	198.0	2019	293	143.6500	105.42
3382	Realme	Android	16.03	yes	no	NaN	13.0	64.0	4.0	5000.0	198.0	2019	299	143.6500	95.52
3344	Motorola	Android	15.88	yes	no	NaN	16.0	64.0	4.0	5000.0	197.0	2020	202	147.9510	109.73
3487	Motorola	Android	15.88	yes	no	NaN	16.0	64.0	4.0	5000.0	197.0	2020	364	147.9510	94.40
1020	Coolpad	Android	15.56	yes	no	NaN	8.0	64.0	4.0	4000.0	177.0	2018	655	149.4700	59.75
368	Realme	Android	16.03	yes	no	NaN	16.0	128.0	4.0	5000.0	199.0	2020	362	150.0200	98.10
143	Realme	Android	16.03	yes	no	NaN	16.0	128.0	4.0	5000.0	199.0	2020	338	150.5300	98.59
3417	Xiaomi	Android	25.88	yes	no	NaN	16.0	64.0	4.0	5020.0	209.0	2020	96	157.4710	121.89
160	Vivo	Android	23.65	yes	no	NaN	16.0	64.0	4.0	5000.0	204.1	2020	246	159.0000	118.22
3385	Realme	Android	15.72	yes	no	NaN	16.0	64.0	4.0	4035.0	184.0	2019	538	159.8850	79.92
3528	Realme	Android	15.72	yes	no	NaN	16.0	64.0	4.0	4035.0	184.0	2019	433	159.8850	80.00
418	Coolpad	Android	20.96	yes	no	NaN	13.0	32.0	3.0	4000.0	170.0	2019	342	161.6100	105.36
3342	Motorola	Android	15.88	yes	no	NaN	16.0	128.0	4.0	4000.0	192.0	2020	186	165.7500	121.79
3485	Motorola	Android	15.88	yes	no	NaN	16.0	128.0	4.0	4000.0	192.0	2020	176	165.7500	124.07
3338	Motorola	Android	15.88	yes	no	NaN	8.0	32.0	3.0	4000.0	189.4	2020	349	169.9915	111.11
3481	Motorola	Android	15.88	yes	no	NaN	8.0	32.0	3.0	4000.0	189.4	2020	101	169.9915	125.64
3408	Xiaomi	Android	23.65	yes	no	NaN	13.0	128.0	4.0	5020.0	199.0	2020	354	169.9915	111.07
3384	Realme	Android	15.88	yes	no	NaN	16.0	64.0	4.0	4000.0	183.0	2019	264	174.1650	132.17
3527	Realme	Android	15.88	yes	no	NaN	16.0	64.0	4.0	4000.0	183.0	2019	503	174.1650	86.88
326	Meizu	Android	16.03	yes	no	NaN	8.0	32.0	2.0	4000.0	184.0	2019	198	179.7600	133.41
101	Meizu	Android	16.03	yes	no	NaN	8.0	32.0	2.0	4000.0	184.0	2019	190	180.4000	137.75
198	Xiaomi	Android	25.88	yes	no	NaN	32.0	64.0	6.0	5020.0	209.0	2020	256	181.0400	131.59
163	Vivo	Android	22.70	yes	no	NaN	8.0	128.0	4.0	5000.0	197.0	2020	118	190.5000	142.28
3410	Xiaomi	Android	25.88	yes	no	NaN	16.0	64.0	6.0	5020.0	209.0	2020	284	192.9500	130.25
2782	Sony	Android	13.81	yes	no	NaN	8.0	32.0	4.0	3300.0	156.0	2019	195	198.1500	149.10
2291	Panasonic	Android	18.26	yes	no	NaN	8.0	64.0	4.0	4000.0	169.0	2018	487	199.0800	99.55
201	Xiaomi	Android	25.88	yes	no	NaN	16.0	64.0	6.0	4500.0	208.0	2020	169	199.4400	151.23
1858	Meizu	Android	15.56	yes	no	NaN	20.0	64.0	4.0	4000.0	170.0	2019	295	199.5600	138.09
367	Realme	Android	16.03	yes	no	NaN	16.0	64.0	4.0	4300.0	191.0	2020	97	200.3200	144.67
195	Xiaomi	Android	24.29	yes	yes	NaN	16.0	64.0	6.0	4520.0	205.0	2020	301	200.6000	128.76
142	Realme	Android	16.03	yes	no	NaN	16.0	64.0	4.0	4300.0	191.0	2020	289	200.7500	145.74
3380	Realme	Android	24.29	yes	yes	NaN	8.0	64.0	6.0	4200.0	202.0	2020	201	203.9915	152.38
3523	Realme	Android	24.29	yes	yes	NaN	8.0	64.0	6.0	4200.0	202.0	2020	282	203.9915	135.78
3520	Realme	Android	16.19	yes	no	NaN	8.0	64.0	6.0	4300.0	202.0	2020	231	211.6500	158.86
3377	Realme	Android	16.19	yes	no	NaN	8.0	64.0	6.0	4300.0	202.0	2020	347	211.6500	137.91
3397	Vivo	Android	23.65	yes	no	NaN	16.0	128.0	8.0	5000.0	197.0	2020	108	212.4830	157.19
3343	Motorola	Android	15.88	yes	no	NaN	16.0	64.0	4.0	5000.0	199.0	2020	97	212.4915	157.45
3486	Motorola	Android	15.88	yes	no	NaN	16.0	64.0	4.0	5000.0	199.0	2020	156	212.4915	159.42
103	Meizu	Android	15.56	yes	no	NaN	16.0	64.0	6.0	4000.0	165.0	2019	517	218.9100	109.51
328	Meizu	Android	15.56	yes	no	NaN	16.0	64.0	6.0	4000.0	165.0	2019	499	220.4400	110.20
3412	Xiaomi	Android	22.70	yes	no	NaN	16.0	64.0	6.0	5260.0	204.0	2020	200	226.0915	168.83
3375	Realme	Android	24.29	yes	yes	NaN	8.0	128.0	6.0	4200.0	194.0	2020	232	234.6935	174.56
3518	Realme	Android	24.29	yes	yes	NaN	8.0	128.0	6.0	4200.0	194.0	2020	258	234.6935	165.37
3395	Vivo	Android	23.65	yes	yes	NaN	16.0	128.0	8.0	4500.0	190.0	2020	197	246.4830	185.34
3414	Xiaomi	Android	24.29	yes	yes	NaN	16.0	64.0	6.0	4160.0	192.0	2020	351	246.6785	159.48
196	Xiaomi	Android	25.88	yes	yes	NaN	16.0	128.0	6.0	4800.0	208.0	2020	319	250.4200	163.38
325	Meizu	Android	16.03	yes	no	NaN	16.0	128.0	6.0	4500.0	183.0	2019	348	251.1900	164.23
100	Meizu	Android	16.03	yes	no	NaN	16.0	128.0	6.0	4500.0	183.0	2019	449	251.2200	125.57
3398	Vivo	Android	24.29	yes	yes	NaN	16.0	128.0	6.0	5000.0	201.0	2020	135	252.8665	188.48
197	Xiaomi	Android	25.88	yes	yes	NaN	16.0	128.0	6.0	4500.0	208.0	2020	184	260.8100	196.45
166	Vivo	Android	22.22	yes	no	NaN	32.0	128.0	8.0	4500.0	176.0	2020	199	270.2100	204.63
3388	Sony	Android	15.24	yes	no	NaN	8.0	128.0	4.0	3600.0	151.0	2020	349	271.1500	174.88
194	Xiaomi	Android	24.29	yes	yes	NaN	20.0	128.0	8.0	4520.0	208.0	2020	318	288.3700	188.10
353	Oppo	Android	24.29	yes	yes	NaN	32.0	128.0	6.0	4000.0	184.0	2020	122	289.4600	218.71
128	Oppo	Android	24.29	yes	yes	NaN	32.0	128.0	6.0	4000.0	184.0	2020	100	290.8600	215.75
3396	Vivo	Android	24.29	yes	yes	NaN	16.0	128.0	6.0	4500.0	195.0	2020	352	293.2330	189.81
3413	Xiaomi	Android	24.29	yes	yes	NaN	16.0	64.0	6.0	4160.0	192.0	2020	156	296.6415	222.63
335	Motorola	Android	16.03	yes	no	NaN	16.0	128.0	6.0	5000.0	210.0	2020	92	298.0600	222.31
736	Asus	Android	19.37	yes	no	NaN	8.0	32.0	4.0	4000.0	165.0	2019	524	299.2700	149.68
162	Vivo	Android	21.27	yes	no	NaN	16.0	128.0	8.0	4500.0	190.2	2020	300	299.7000	195.05
110	Motorola	Android	16.03	yes	no	NaN	16.0	128.0	6.0	5000.0	210.0	2020	242	300.3200	222.49
863	BlackBerry	Android	28.42	yes	no	NaN	16.0	64.0	4.0	4000.0	170.0	2018	383	301.6600	194.68
737	Asus	Android	19.37	yes	no	NaN	8.0	64.0	4.0	4000.0	165.0	2019	397	310.5300	201.16
211	ZTE	Android	25.56	yes	yes	NaN	12.0	128.0	6.0	5100.0	210.0	2020	278	311.1100	209.72
159	Vivo	Android	22.22	yes	no	NaN	32.0	128.0	8.0	4500.0	176.0	2020	343	319.4800	206.54
861	BlackBerry	Android	10.95	yes	no	NaN	8.0	32.0	4.0	3000.0	156.0	2018	552	331.0600	165.55
3365	Oppo	Android	15.88	yes	yes	NaN	32.0	128.0	8.0	4025.0	180.0	2020	306	339.1500	219.57
3508	Oppo	Android	15.88	yes	yes	NaN	32.0	128.0	8.0	4025.0	180.0	2020	326	339.1500	218.95
102	Meizu	Android	15.56	yes	no	NaN	20.0	128.0	6.0	3600.0	166.0	2019	459	340.5900	170.34
327	Meizu	Android	15.56	yes	no	NaN	20.0	128.0	6.0	3600.0	166.0	2019	405	341.1600	170.70
862	BlackBerry	Android	28.42	yes	no	NaN	16.0	64.0	4.0	4000.0	170.0	2018	629	348.2900	139.37
2292	Panasonic	Android	18.10	yes	no	NaN	16.0	128.0	4.0	3000.0	195.0	2018	717	349.4000	139.60
164	Vivo	Android	24.29	yes	yes	NaN	16.0	128.0	6.0	4500.0	198.1	2020	312	349.8300	227.88
2781	Sony	Android	15.24	yes	no	NaN	8.0	64.0	4.0	2870.0	162.0	2019	235	351.6300	262.70
3409	Xiaomi	Android	25.88	yes	yes	NaN	16.0	128.0	6.0	4700.0	219.0	2020	128	358.7000	272.45
417	Coolpad	Android	23.65	yes	yes	NaN	16.0	64.0	4.0	4000.0	195.0	2020	252	359.7700	258.53
3526	Realme	Android	16.03	yes	no	NaN	16.0	64.0	6.0	4000.0	199.0	2019	181	365.4150	273.29
3383	Realme	Android	16.03	yes	no	NaN	16.0	64.0	6.0	4000.0	199.0	2019	475	365.4150	182.74
127	Oppo	Android	22.07	yes	yes	NaN	32.0	128.0	8.0	4000.0	183.0	2020	271	368.8000	260.19
352	Oppo	Android	22.07	yes	yes	NaN	32.0	128.0	8.0	4000.0	183.0	2020	281	369.3000	257.34
3363	OnePlus	Android	23.97	yes	no	NaN	16.0	128.0	8.0	3800.0	190.0	2019	381	382.4915	249.32
3506	OnePlus	Android	23.97	yes	no	NaN	16.0	128.0	8.0	3800.0	190.0	2019	476	382.4915	191.21
3389	Sony	Android	15.40	yes	no	NaN	8.0	128.0	6.0	3140.0	164.0	2019	348	392.6915	254.39
3374	Realme	Android	22.22	yes	yes	NaN	8.0	128.0	6.0	4200.0	209.0	2020	148	395.2415	298.10
3517	Realme	Android	22.22	yes	yes	NaN	8.0	128.0	6.0	4200.0	209.0	2020	219	395.2415	297.12
131	Oppo	Android	15.88	yes	yes	NaN	32.0	128.0	8.0	4025.0	180.0	2020	146	398.7700	297.87
356	Oppo	Android	15.88	yes	yes	NaN	32.0	128.0	8.0	4025.0	180.0	2020	218	399.5500	299.98
3416	Xiaomi	Android	25.88	yes	yes	NaN	16.0	128.0	6.0	4700.0	218.0	2020	306	413.0915	270.33
104	Meizu	Android	15.56	yes	no	NaN	20.0	128.0	6.0	3600.0	165.0	2019	332	420.1700	272.02
329	Meizu	Android	15.56	yes	no	NaN	20.0	128.0	6.0	3600.0	165.0	2019	226	421.1200	318.15
2780	Sony	Android	16.03	yes	no	NaN	8.0	64.0	4.0	3000.0	180.0	2019	252	429.1000	295.97
126	Oppo	Android	23.97	yes	yes	NaN	32.0	128.0	8.0	4000.0	172.0	2020	187	470.3400	356.01
351	Oppo	Android	23.97	yes	yes	NaN	32.0	128.0	8.0	4000.0	172.0	2020	293	470.8100	335.09
3421	Xiaomi	Android	25.88	yes	yes	NaN	20.0	128.0	8.0	4780.0	208.0	2020	321	472.5915	308.77
3521	Realme	Android	22.22	yes	yes	NaN	8.0	128.0	6.0	4200.0	205.0	2020	141	480.7430	359.14
3378	Realme	Android	22.22	yes	yes	NaN	8.0	128.0	6.0	4200.0	205.0	2020	257	480.7430	342.84
3399	Vivo	Android	22.22	yes	yes	NaN	16.0	128.0	6.0	4400.0	214.5	2020	154	488.6650	363.41
3441	ZTE	Android	25.56	yes	yes	NaN	8.0	128.0	8.0	4500.0	218.0	2020	133	492.1500	369.60
2205	OnePlus	Android	13.49	yes	no	NaN	16.0	128.0	4.0	3300.0	153.0	2017	875	499.2100	149.69
2204	OnePlus	Android	15.40	yes	no	NaN	16.0	128.0	4.0	3300.0	162.0	2017	623	500.1800	199.99
3419	Xiaomi	Android	25.88	yes	yes	NaN	20.0	128.0	8.0	4720.0	222.0	2020	164	500.6500	377.16
864	BlackBerry	Android	10.95	yes	no	NaN	8.0	64.0	4.0	3500.0	168.0	2018	471	501.4200	250.66
3507	Oppo	Android	16.03	yes	yes	NaN	32.0	256.0	12.0	4025.0	171.0	2020	348	509.1500	328.72
3440	ZTE	Android	22.70	yes	yes	NaN	20.0	128.0	6.0	4000.0	168.0	2020	217	509.1500	379.80
3364	Oppo	Android	16.03	yes	yes	NaN	32.0	256.0	12.0	4025.0	171.0	2020	227	509.1500	380.74
3415	Xiaomi	Android	25.88	yes	yes	NaN	16.0	128.0	8.0	4700.0	218.0	2020	194	518.4915	386.79
2203	OnePlus	Android	19.69	yes	no	NaN	16.0	128.0	4.0	3300.0	177.0	2018	386	519.3800	336.78
129	Oppo	Android	23.97	yes	yes	NaN	16.0	128.0	8.0	4000.0	186.0	2020	186	519.8200	391.59
354	Oppo	Android	23.97	yes	yes	NaN	16.0	128.0	8.0	4000.0	186.0	2020	200	520.1600	388.72
324	Meizu	Android	16.19	yes	yes	NaN	20.0	128.0	8.0	4500.0	199.0	2020	318	529.2900	344.66
99	Meizu	Android	16.19	yes	yes	NaN	20.0	128.0	8.0	4500.0	199.0	2020	186	529.5500	398.56
3394	Vivo	Android	24.13	yes	yes	NaN	32.0	128.0	8.0	4315.0	181.5	2020	165	545.5725	407.09
2202	OnePlus	Android	21.75	yes	no	NaN	16.0	256.0	4.0	3700.0	185.0	2018	496	549.7400	274.99
3362	OnePlus	Android	25.88	yes	no	NaN	16.0	256.0	8.0	4085.0	206.0	2019	341	551.6075	358.34
3505	OnePlus	Android	25.88	yes	no	NaN	16.0	256.0	8.0	4085.0	206.0	2019	367	551.6075	359.07
210	ZTE	Android	25.56	yes	yes	NaN	12.0	256.0	8.0	5100.0	215.0	2020	235	598.6600	448.34
3480	Meizu	Android	16.19	yes	yes	NaN	20.0	128.0	8.0	4500.0	219.0	2020	139	600.0915	451.07
3337	Meizu	Android	16.19	yes	yes	NaN	20.0	128.0	8.0	4500.0	219.0	2020	261	600.0915	412.08
161	Vivo	Android	24.13	yes	yes	NaN	32.0	128.0	8.0	4315.0	181.5	2020	145	630.2500	470.69
165	Vivo	Android	29.37	yes	yes	NaN	16.0	256.0	8.0	4500.0	219.5	2020	226	630.9900	472.89
123	OnePlus	Android	23.97	yes	yes	NaN	16.0	128.0	8.0	4300.0	180.0	2020	208	648.1400	490.04
348	OnePlus	Android	23.97	yes	yes	NaN	16.0	128.0	8.0	4300.0	180.0	2020	232	651.0100	489.18
3566	Asus	Android	15.88	yes	no	NaN	8.0	64.0	6.0	5000.0	190.0	2019	232	654.5000	490.96
3418	Xiaomi	Android	17.94	yes	yes	NaN	20.0	256.0	8.0	5000.0	253.0	2020	361	671.4915	436.77
2201	OnePlus	Android	21.75	yes	no	NaN	16.0	256.0	4.0	3700.0	185.0	2018	489	700.9400	350.47
3420	Xiaomi	Android	25.88	yes	yes	NaN	20.0	256.0	8.0	4500.0	208.0	2020	112	713.9915	535.92
347	OnePlus	Android	23.97	yes	yes	NaN	16.0	128.0	8.0	4300.0	180.0	2020	186	738.8200	553.77
122	OnePlus	Android	23.97	yes	yes	NaN	16.0	128.0	8.0	4300.0	180.0	2020	110	741.9700	559.03
350	OnePlus	Android	25.88	yes	yes	NaN	16.0	128.0	6.0	4000.0	206.0	2019	523	799.8000	400.00
349	OnePlus	Android	25.88	yes	yes	NaN	16.0	256.0	12.0	4085.0	206.0	2019	280	800.9200	553.59
124	OnePlus	Android	25.88	yes	yes	NaN	16.0	256.0	12.0	4085.0	206.0	2019	458	801.2400	400.43
125	OnePlus	Android	25.88	yes	yes	NaN	16.0	128.0	6.0	4000.0	206.0	2019	294	801.6300	568.56
3367	Oppo	Android	16.35	yes	yes	NaN	32.0	128.0	8.0	4200.0	209.0	2020	91	824.4915	613.87
3510	Oppo	Android	16.35	yes	yes	NaN	32.0	128.0	8.0	4200.0	209.0	2020	261	824.4915	566.32
3387	Sony	Android	16.03	yes	yes	NaN	8.0	256.0	8.0	4000.0	181.4	2020	236	934.1500	698.61
3509	Oppo	Android	16.35	yes	yes	NaN	32.0	256.0	12.0	4260.0	217.0	2020	159	934.9915	702.85
3366	Oppo	Android	16.35	yes	yes	NaN	32.0	256.0	12.0	4260.0	217.0	2020	193	934.9915	699.64
2779	Sony	Android	16.03	yes	no	NaN	8.0	64.0	4.0	3330.0	180.0	2019	328	999.7400	650.33
3565	Asus	Android	24.61	yes	no	NaN	24.0	128.0	8.0	6000.0	240.0	2019	325	1163.6500	756.99
336	Motorola	Android	16.35	yes	yes	NaN	25.0	256.0	12.0	5000.0	203.0	2020	188	1197.4900	894.04
111	Motorola	Android	16.35	yes	yes	NaN	25.0	256.0	12.0	5000.0	203.0	2020	220	1200.8500	901.27

		main_camera_mp	selfie_camera_mp	new_price
release_year	brand_name
2018	Acer	5.0	2.0	328.3200
	Alcatel	13.0	8.0	230.4500
	Apple	12.0	7.0	1250.3200
	Asus	13.0	8.0	949.2700
	BlackBerry	NaN	16.0	501.4200
	Coolpad	NaN	8.0	149.4700
	Gionee	8.0	5.0	131.6300
	Google	12.2	NaN	959.0800
	HTC	13.0	13.0	650.8800
	Honor	13.0	25.0	570.6800
	Huawei	13.0	25.0	1600.2900
	LG	16.0	8.0	802.0100
	Lenovo	13.0	16.0	400.4400
	Meizu	16.0	20.0	481.4200
	Motorola	13.0	12.0	399.5400
	Nokia	16.0	20.0	549.8200
	OnePlus	NaN	16.0	700.9400
	Oppo	16.0	25.0	1352.4200
	Others	16.0	20.0	899.9500
	Panasonic	NaN	16.0	349.4000
	Realme	13.0	25.0	210.6000
	Samsung	16.0	24.0	748.9900
	Sony	23.0	13.0	898.4000
	Vivo	13.0	25.0	700.7800
	Xiaomi	13.0	24.0	559.3300
	ZTE	24.0	20.0	650.7800
2019	Alcatel	5.0	8.0	150.8100
	Apple	8.0	7.0	849.1700
	Asus	NaN	24.0	1163.6500
	Coolpad	NaN	13.0	161.6100
	Google	12.2	8.0	577.1500
	HTC	13.0	16.0	419.8800
	Honor	13.0	32.0	501.7600
	Huawei	13.0	32.0	2300.8700
	Infinix	NaN	16.0	130.4900
	LG	16.0	32.0	1100.3100
	Lenovo	13.0	32.0	402.0700
	Meizu	NaN	20.0	421.1200
	Motorola	48.0	25.0	298.1700
	Nokia	13.0	20.0	619.7000
	OnePlus	NaN	16.0	801.6300
	Oppo	8.0	32.0	880.8000
	Others	22.6	24.0	900.8700
	Realme	NaN	25.0	365.4150
	Samsung	16.0	32.0	1751.1800
	Sony	NaN	8.0	999.7400
	Vivo	13.0	32.0	731.3300
	Xiaomi	13.0	32.0	2498.2400
	ZTE	48.0	20.0	819.5700
2020	Alcatel	13.0	5.0	101.9150
	Apple	12.0	7.0	999.5800
	Coolpad	NaN	16.0	359.7700
	Honor	13.0	32.0	634.0915
	Huawei	13.0	32.0	2560.2000
	Infinix	NaN	8.0	111.2500
	LG	8.0	16.0	870.0100
	Lava	NaN	5.0	79.9400
	Lenovo	8.0	5.0	181.5200
	Meizu	NaN	20.0	600.0915
	Motorola	NaN	25.0	1200.8500
	Nokia	8.0	24.0	501.1200
	OnePlus	NaN	16.0	741.9700
	Oppo	NaN	32.0	934.9915
	Others	13.0	24.0	670.6800
	Realme	NaN	16.0	480.7430
	Samsung	8.0	32.0	1054.4505
	Sony	NaN	8.0	934.1500
	Vivo	NaN	32.0	630.9900
	Xiaomi	NaN	32.0	713.9915
	ZTE	NaN	20.0	598.6600

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
2186	Nokia	Windows	10.95	yes	no	41.0	1.2	32.0	4.0	2000.0	158.0	2013	988	399.1300	119.75
216	ZTE	Android	25.56	yes	no	48.0	16.0	128.0	8.0	5000.0	215.0	2019	336	819.5700	533.34
221	ZTE	Android	25.56	yes	no	48.0	16.0	64.0	6.0	5000.0	215.0	2019	506	501.5600	250.83
3354	Motorola	Android	15.88	yes	no	48.0	25.0	128.0	4.0	3600.0	165.0	2019	371	254.9915	164.69
3497	Motorola	Android	15.88	yes	no	48.0	25.0	128.0	4.0	3600.0	165.0	2019	422	254.9915	127.72

	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
0	23.89	1	0	13.0	5.0	64.0	3.0	3020.0	146.0	2020	127	111.62	86.96
1	23.89	1	1	13.0	16.0	128.0	8.0	4300.0	213.0	2020	325	249.39	161.49
2	23.89	1	1	13.0	8.0	128.0	8.0	4200.0	213.0	2020	162	359.47	268.55
3	23.89	1	1	13.0	8.0	64.0	6.0	7250.0	272.0	2020	345	278.93	180.23
4	15.72	1	0	13.0	8.0	64.0	3.0	5000.0	185.0	2020	293	140.87	103.80

	feature	VIF
0	screen_size	32.442367
1	4g	5.520042
2	5g	1.690646
3	main_camera_mp	9.938121
4	selfie_camera_mp	6.041559
5	int_memory	4.053550
6	ram	15.128273
7	battery	22.075739
8	weight	40.634631
9	release_year	50.048518
10	days_used	14.357589
11	new_price	6.458663

	feature	VIF
0	screen_size	29.066443
1	4g	5.284076
2	5g	1.688539
3	main_camera_mp	9.876165
4	selfie_camera_mp	6.035672
5	int_memory	4.052941
6	ram	15.127731
7	weight	29.104788
8	release_year	48.779558
9	days_used	14.232892
10	new_price	6.448631

	feature	VIF
0	screen_size	27.857051
1	4g	5.497355
2	5g	1.690634
3	main_camera_mp	9.654145
4	selfie_camera_mp	5.964633
5	int_memory	4.053125
6	ram	15.125880
7	battery	15.811876
8	release_year	45.706727
9	days_used	14.187948
10	new_price	6.406424

	Actual Values	Fitted Values	Residuals
1472	68.37	68.202828	0.167172
127	260.19	219.193721	40.996279
907	44.88	38.672646	6.207354
2200	92.35	96.114753	-3.764753
1216	74.99	95.425720	-20.435720

Importing necessary libraries and data¶

Data Overview¶

Questions¶

FIRST LOOK¶

Initial Observations¶

Exploratory Data Analysis (EDA)¶

Observation: Most used phones are under 500 Euros and there appears to be some cosing 2000¶

The top available brands are Samsung, Huawei, LG, and Lenovo¶

Observation: It looks like 4GB RAM phones from older years are still available, which could useful for customers on a budget¶

Observation: There appears to be an outlier in the top left. How can a phone with an enormous battery and screen size weigh so little?¶

Observation: There is a positive relationship, but it's not as obvious because most of the main cameras that have 10-12GB have a very wide spread in new price. It also seems like most of the newer models in the dataset stay in the 8-12GB range¶

There are some lightweight phones available with large batteries, but mostly as the battery increases, so does the weight¶

Observation: There is a good amount of availability of phones from many different brands that have screen sizes greater than 6 inches¶

Observations¶

The Selfie Cameras get better year after year, for all operating systems¶

Observation: Why are there 6 distinct lines in the graph above when comparing used price vs new price? And why does it seem somewhat related to year?¶

Observation: A lot of the newer models have been used less so they might be in better condition¶

Observation: The Selfie camera has gotten way better in recent years while the main camera has not¶

Questions¶

Data Preprocessing¶

We already checked for duplicates and there are none. Moving on to check for missing values.¶

Replacing/Dropping missing values and outliers¶

EDA¶

Observation: The correlation values changed but the positive/negative signs did not¶

Observation: Everything looks good and we can tell that outliers were capped. We will build and test the model with and without outlier treatment in the next step¶

Building a Linear Regression model¶

Model performance evaluation¶

Observation: The first model does really well with the testing set at .957¶

Checking Linear Regression Assumptions¶

TEST FOR MULTICOLLINEARITY¶

TEST FOR LINEARITY AND INDEPENDENCE¶

We see no pattern in the plot above. Hence, the assumptions of linearity and independence are satisfied.¶

TEST FOR NORMALITY¶

TEST FOR HOMOSCEDASTICITY¶

Final Model Summary¶

Including all the Coefficients¶

The final linear model captures up to 96% of the test data¶

Here's what we did:¶

Observations¶

Actionable Insights and Recommendations¶